Oscillation

The supremal difference between values of a function over arbitrarily small neighborhoods (local oscillation) or the supremum minus infimum over a set (global oscillation), used to quantify local variability: ω_f(x0) = lim_{r→0} sup_{B(x0,r)} f - inf_{B(x0,r)} f. Oscillation measures failure of continuity and refines modulus of continuity.